Question

What are the zeros of the polynomial function? f(x)=x3+2x2−x−2 Select each correct answer. A.−3 B. −2 C. −1D. 0 E. 1F. 2 G. 3

Answer 1

Answer:

B. −2

C. −1

E.  1

Step-by-step explanation:

He have been given a polynomial function $f(x)=x^3+2x^2-x-2$. We are asked to find the zeros of our given function.

To find the zeros of our given function, we will equate our function with zero and solve for x as:

$x^3+2x^2-x-2=0$

Now, we will factor our equation by grouping method.

$(x^3+2x^2)-(x+2)=0$

$x^2(x+2)-1(x+2)=0$

$(x+2)(x^2-1)=0$

Now, we will use difference of squares $a^b-b^2=(a+b)(a-b)$

$(x+2)(x^2-1^2)=0$

$(x+2)(x+1)(x-1)=0$

Using zero product property, we will get:

$(x+2)=0\text{ or }(x+1)=0\text{ or }(x-1)=0$

$x=-2\text{ or }x=-1\text{ or }x=1$

Since the zeros of our given function are $-2,-1\text{ and }1$, therefore, options B, C and E are correct choices.